Summer Assignment for Miss Kiker’s Geometry
1. Read the first 4 pages.
2. Print the last 2 pages and solve the problems. You must
show your work or you will not receive credit.
3. Hand in your work the first day of class.
4. Have a good summer!
Things you should know.
Simplifying radicals without your calculator.
A sq root is simplified when the following conditions are met:
–
1.) The radicand has no factor other than 1 that is a perfect sq
–
2) The radicand does not contain a fraction
–
3) No radical appears in the denominator of a fraction
Example 1
Example 2
Example 3
page1
Solving systems of equations
Substitution
The substitution method is used to eliminate one of the variables by replacement when solving a system
of equations.
Solve this system of equations
3y - 2x = 11
y + 2x = 9
1. Solve one of the equations for either "x =" or "y =".
This example solves the second equation for "y =".
3y - 2x = 11
y = 9 - 2x
2. Replace the "y" value in the first equation by what
"y" now equals.
3(9 - 2x) - 2x = 11
3. Solve this new equation for "x".
(27 - 6x) - 2x = 11
27 - 6x - 2x = 11
27 - 8x = 11
-8x = -16
x=2
page2
Solving using elimination
Another way of solving a linear system is to use the elimination method. In
the elimination method you either add or subtract the equations to get an equation in one
variable.
2x – y = 9
3x + 4y = –14
Nothing cancels here, but I can multiply to create a cancellation. I can multiply the first equation
by 4, and this will set up the y-terms to cancel.
Multiply
by 4
Solving this, I get that x
= 2. I'll use the first equation, because the coefficients are smaller.
2(2) – y = 9
4–y=9
–y = 5
y = –5
The solution is (x,
y) = (2, –5).
page3
The Quadratic Formula.
The quadratic equation
has the solutions
Example: Use the Quadratic Formula to solve
Solution. We have a=2, b= -3, and
. By the quadratic formula, the solutions are
page4
Name_______________________________________________
Simplify the following without your calculator. Show your work.
1. √50
9. √28𝑝2 𝑞 7 𝑟11
2. √63
10.
√40
√25
11.
√15
4√48
3. √144
4. √128
12.
4√2𝑛5
5√3𝑛2
5. √25√3
13.
6. √15√10
14.
7. √8√6
15.
8. √27𝑥 4 𝑦 5 𝑧 6
page5
√5𝑥
6√3𝑥 4
3
4−2√5
5
7+6√2
Solve using substitution. Show your work.
16) x + y = 3
17) 2x – 3y = -4
3y + x = 5
x + 3y = 7
Solve using elimination. Show your work.
18) 3x – 4y = -27
19) 4x – 3y = 22
2x + y = -7
2x + 8y = 30
Solve by factoring. Show your work.
20) x2 + 13x + 36 = 0
21) x2 – 3x - 40 = 0
22) 3x2 + 15x + 18 = 0
23) 5x4 – 10x3 – 75x2 = 0
Solve using the Quadratic Formula. Show your work.
24) x2 + 2x - 18 = 0
25) 2x2 + 18 x + 39 = 0
page6